1. AI Classnotes #5, John Shieh, 2012
HEURISTIC SEARCH
4.0 Introduction
4.1 An Algorithm for Heuristic Search
4.2 Admissibility, Monotonicity, and Informedness
4.3 Using Heuristics in Games
4.4 Complexity Issues
AI Classnotes #5, John Shieh, 2012

2. AI Classnotes #5, John Shieh, 2012
Fig 4.1 First three levels of the tic-tac-toe state space reduced by symmetry
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Fig 4.2 The “most wins” heuristic applied to the first children in tic-tac-toe.
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Fig 4.3 Heuristically reduced state space for tic-tac-toe.
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Fig 4.4 The local maximum problem for hill-climbing with 3-level look ahead
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Fig 4.10 Heuristic search of a hypothetical state space.
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8. AI Classnotes #5, John Shieh, 2012
A trace of the execution of best_first_search for Figure 4.4
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Fig 4.11 Heuristic search of a hypothetical state space with open and closed states highlighted.
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Fig 4.12 The start state, first moves, and goal state for an example-8 puzzle.
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Fig 4.14 Three heuristics applied to states in the 8-puzzle.
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Fig 4.15 The heuristic f applied to states in the 8-puzzle.
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Fig 4.16 State space generated in heuristic search of the 8-puzzle graph.
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Fig 4.17 Open and closed as they appear after the 3rd iteration of heuristic search
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Fig 4.18 Comparison of state space searched using heuristic search with space searched by breadth-first search. The proportion of the graph searched heuristically is shaded. The optimal search selection is in bold. Heuristic used is f(n) = g(n) + h(n) where h(n) is tiles out of place.
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Fig 4.19 State space for a variant of nim. Each state partitions the seven matches into one or more piles.
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Fig 4.20 Exhaustive minimax for the game of nim. Bold lines indicate forced win for MAX. Each node is marked with its derived value (0 or 1) under minimax.
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Fig 4.21 Minimax to a hypothetical state space. Leafstates show heuristic values; internal states show backed-up values.
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Fig 4.22 Heuristic measuring conflict applied to states of tic-tac-toe.
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Fig 4.23 Two-ply minimax applied to the opening move of tic-tac-toe, from Nilsson (1971).
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Fig 4.24 Two ply minimax, and one of two possible MAX second moves, from Nilsson (1971).
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Fig 4.25 Two-ply minimax applied to X’s move near the end of the game, from Nilsson (1971).
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Fig 4.26 Alpha-beta pruning applied to state space of Fig States without numbers are not evaluated.
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Fig 4.27 Number of nodes generated as a function of branching factor, B, for various lengths, L, of solution paths. The relating equation is T = B(BL – 1)/(B – 1), adapted from Nilsson (1980).
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Luger: Artificial Intelligence, 5th edition. © Pearson Education Limited, 2005 6

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Fig 4.28 Informal plot of cost of searching and cost of computing heuristic evaluation against informedness of heuristic, adapted from Nilsson (1980).
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Fig 4.29 The sliding block puzzle.
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Fig 4.30.
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Fig 4.31.
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